As described, you have the same voltage induced in every turn of the secondary. This is the same throughout the transformer (neglecting minor flux leakages).
But you can have different _currents_ flowing via any of the available paths on the secondary.
Consider a standard center tapped single phase transformer. Depending upon the loads connected to the two legs, you can have different magnitude and phase of the current flowing on the two halves of the winding.
There are points in time where the currents will not have the same sign, even with an end reference.You only appear to have currents flowing in two directions because you choose to use the neutral as your reference point. If you use an end point of a the winding as your reference the currents flow in the same direction.
The number of phases should not depend on if a neutral is or is not used.